We have, $\left|\sqrt{2 \sin ^4 x+18 \cos ^2 x}-\sqrt{2 \cos ^4 x+18 \sin ^2 x}\right|=1$ That is, $f(x)=\left|\sqrt{2 \sin ^4 x+8 \cos ^2 x}-\sqrt{2 \cos ^4 x+18 \sin ^2 x}\right|$ Now, $f(x)=f\left(\frac{\pi}{2}-x\right)$ $\Rightarrow f(x)$ is symmetric about $x=\frac{\pi}{4}$. If $f(x)$ has solution in $(0, \pi / 4)$, then in $(0,2 \pi)$, there are eight solutions.